Question

The amplitude of the magnetic field of a plane electromagnetic wave propagating along the positive X axis in a vacuum is 510 nT`hat k` and its angular frequency is 60 × 10⁶ rad/sec. Write the expression for the electric field `(vec E)`.

Answer 1

Given: B_o = 510 nT = 510 × 10⁻⁹ T

ω = 60 × 10⁶ rad/sec

c = 3 × 10⁸ m/s

E_o = cB_o

= 3 × 10⁸ × 510 × 10⁻⁹

= 153 N/C

k = `ω/c`

= `(60 xx 10^6)/(3 xx 10^8)`

= 20 × 10⁻² rad/m

The general expression for the electric field of a plane electromagnetic wave propagating along the x-axis is

`vec E(x, t) = E_o sin(omega t - kx)`

= 153 sin(60 × 10⁶ t − 20 × 10⁻² x) N/C